On the day his grandson was born, a man deposited to a trust company a sufficient amount of money so that the boy could receive five annual payments of P10,000 each for his college tuition fees

Question

On the day his grandson was born, a man deposited to a trust company a sufficient amount of money so that the boy could receive five annual payments of P10,000 each for his college tuition fees, starting on his 18th birthday. Interest rate of 13.6% per annum was to be paid on all amounts on deposit. There was also a provision that the grandson could elect to withdraw no annual payments and receive a single lump sum amount on his 25th birthday. The grandson chose this option.

1. How much did the boy receive as the single payment?

2. How much did the grandfather deposit?

Answer 1

To calculate the single lump sum payment the grandson received on his 25th birthday, we need to find the present value of the five annual payments of P10,000 each, discounted at an interest rate of 13.6% per annum.

We can use the formula for the present value of an ordinary annuity:

PV = PMT × [(1 - (1 + r)^(-n)) / r],

where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, PMT = P10,000, r = 13.6% = 0.136, and n = 5.

Using these values, we can calculate the present value:

PV = P10,000 × [(1 - (1 + 0.136)^(-5)) / 0.136] ≈ P10,000 × [0.746]

PV ≈ P7,460.

Therefore, the boy received a single payment of P7,460 on his 25th birthday.

Now, to determine how much the grandfather deposited, we need to calculate the future value of the single payment of P10,000 on the boy's 18th birthday, compounded annually at an interest rate of 13.6% per annum, for a period of 7 years.

We can use the formula for the future value of a single sum:

FV = PV × (1 + r)^n,

where FV is the future value, PV is the present value, r is the interest rate per period, and n is the number of periods.

In this case, PV = P10,000, r = 13.6% = 0.136, and n = 7.

Using these values, we can calculate the future value:

FV = P10,000 × (1 + 0.136)^7 ≈ P10,000 × (1.136)^7 ≈ P10,000 × 1.9473

FV ≈ P19,473.

Therefore, the grandfather deposited approximately P19,473.